One good empirical test will be Georgia's U.S. Senate runoff election on December 6, 2022. In the first round of election the results were as follows:
In the second round, Libertarian candidate Chase Oliver will be eliminated, so the percentage vote totals in the runoff election in excess of the first round results for Raphael Warnock and Herschel Walker will be a good approximation of how the Libertarian vote split.
Of course, in this case, as in most cases, two successive elections don't have exactly the same voters and differences in voter turnout between elections can obscure shifts in the Libertarian vote from one election to another.
An alternative is to look at a race, like this one in Georgia that has a Libertarian candidate, and to also look at other races without a significant third-party candidate running on the same day in the same election involving similar issues (e.g. a tight Congressional race in Georgia between a Democrat and a Republican with no third party candidate). Then you can compare the vote totals for the two party race and the three party race in the same geographic area (e.g. a county total) to try to estimate the effect in that case. The raw data from the Georgia Secretary of State is here if you want to analyze it in the context of the "natural experiment" of the 2022 midterms in Georgia.
For example, U.S. House District 2 in Georgia was a reasonably close race with only a Democrat and a Republican running.
Previous studies (I'll cite chapter and verse if I can find them easily) have shown that while some people who vote for third-party candidates would vote for a major party candidate if the third-party candidate were not available, that a significant share of third-party voters, on the order of 20%-60%, would not vote for either a Democrat or a Republican if the third-party candidate were not an option. So, that has to be figured into the "lean" of the third-party vote as well.
Further, as the answer from @JamesK observes, third-party voters may be swayed by the individual candidates rather than their party affiliation. Thus, in the Georgia U.S. Senate race, for example, Libertarian voters who chose to vote in the runoff election may be basing their decisions more on their assessments of Raphael Warnock and Herschel Walker as individuals rather than based upon their partisan affiliation.